For Exercises 35–44, an equation of a parabola
or
is given.
a. Identify the vertex, value of p, focus, and focal diameter of the parabola.
b. Identify the endpoints of the latus rectum.
c. Graph the parabola.
d. Write equations for the directrix and axis of symmetry. (See Example 4)
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College Algebra (Collegiate Math)
- In Exercises 5–12, find the standard form of the equation of each hyperbola satisfying the given conditions. 5. Foci: (0, –3), (0, 3); vertices: (0, –1), (0, 1) 6. Foci: (0, –6), (0, 6); vertices: (0, -2), (0, 2) 7. Foci: (-4, 0), (4, 0); vertices: (-3, 0), (3,0) 8. Foci: (-7, 0), (7, 0); vertices: (-5, 0), (5,0) 9. Endpoints of transverse axis: (0, -6), (0, 6); asymptote: y = 2x 10. Endpoints of transverse axis: (-4,0), (4, 0); asymptote: y = 2r 11. Center: (4, -2); Focus: (7, -2); vertex: (6, -2) 12. Center: (-2, 1); Focus: (-2, 6); vertex: (-2, 4)arrow_forward1. A parabola has equation - 12x + y² – 24 = 0. Write the equation in standard form.arrow_forwardExercises 98–100 will help you prepare for the material covered in the first section of the next chapter. 98. a. Does (-5, –6) satisfy 2x – y = -4? b. Does (-5, -6) satisfy 3x – 5y = 15? 99. Graph y = -x – 1 and 4x – 3y = 24 in the same rectangular coordinate system. At what point do the graphs intersect? 100. Solve: 7x – 2(-2x + 4) = 3.arrow_forward
- 7. Write an equation for each parabola. a) (0, 11) 4 (4, –5) b) YA (-6, 4) 4 (-5,3) -6 -2 0 x c) YA 12 (4,13) 14 +4 (6, –7) -carrow_forward2. Obtain the graph of the parabola y = -x² + 4x using transformations of the graph of y = x². Explain each step.arrow_forward(b) Find an equation for the parabola that has axis x = -1 and passes [3] through the points (4,5) and (0,–7). Sketch the parabola and identify the directrix.arrow_forward
- Write an equation of the parabola with its vertex at (x, y)- (3, 9) and focus at (x, y) (3, -2).arrow_forwardThe location of the focus of the parabola x2 – 6x – 12y – 51 = 0 is at a. (2, -3) b. (3, -5) c. (2, -5) d. (3, -2)arrow_forwardFind the equation of the parabola with V(-2,-3) and a directrex y=-7arrow_forward
- In Exercises 17-30, find the standard form of the equation of each parabola satisfying the given conditions. 17. Focus: (7,0); Directrix: x = -7 18. Focus: (9,0); Directrix: x = -9 19. Focus: (-5,0); Directrix: x = 5 20. Focus: (-10, 0); Directrix: x = 10 21. Focus: (0, 15); Directrix: y = -15 22. Focus: (0,20); Directrix: y = -20 23. Focus: (0, –25); Directrix: y = 25 24. Focus: (0, -15); Directrix: y = 15 25. Vertex: (2, -3); Focus: (2, -5) 26. Vertex: (5, -2); Focus: (7, -2) 27. Focus: (3, 2); Directrix: x = -1 28. Focus: (2, 4); Directrix: x = -4 29. Focus: (-3, 4); Directrix: y = 2 30. Focus: (7, –1); Directrix: y = -9arrow_forward5 Identify the vertex of the parabola: 0/1 X Y -5 -7 -4 -3 -2 8. -1 9. 8 1 2arrow_forward
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